It is given that $\angle XYZ = 64^o$ and $XY$ is produced to point $P$. If ray $YQ$ bisects $\angle ZYP$,find $\angle XYQ$ and reflex $\angle QYP$. (in $^o$)

In the figure,lines $AB$ and $CD$ intersect at $O$. If $\angle AOC + \angle BOE = 70^o$ and $\angle BOD = 40^o$,find $\angle BOE$ and reflex $\angle COE$.

In the figure,if $x+y=w+z$,then prove that $AOB$ is a line.

Let $OA, OB, OC$ and $OD$ be rays in the anticlockwise direction such that $\angle AOB = 100^{\circ}, \angle COD = 100^{\circ}, \angle BOC = 82^{\circ}$ and $\angle AOD = 78^{\circ}$. Is it true to say that $AOC$ and $BOD$ are lines?

In the figure,$POQ$ is a line. Ray $OR$ is perpendicular to line $PQ$. $OS$ is another ray lying between rays $OP$ and $OR$. Prove that $\angle ROS = \frac{1}{2}(\angle QOS - \angle POS)$.

An angle which is greater than $180^{\circ}$ but less than $360^{\circ}$ is called a $\ldots \ldots \ldots .$.